Finite Group Databasebeta

← Group #271051

Character table — Group #271051

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444442222224444444422444444448888888888888888224444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-11-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-11-1-111-1-11-1
χ611111111111111111111-1-11-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-11-1-1-1-111-11
χ711111111111111111111-1-11-1-1-1-1-1-11-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11-111-1-111-11
χ811111111111111111111-1-11-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11-11111-1-11-1
χ91111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ101111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ131111111111111111-1-1-1-1-1-11-1-1-1-1-1-1111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1111-1-1111-1
χ141111111111111111-1-1-1-1-1-11-1-1-1-1-1-1111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-111111-1-1-11
χ151111111111111111-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-11111111-1-1-111-1-1-11
χ161111111111111111-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-1111111-1-1-1-111111111-1-1-1-1111-1-1-1-1-1111-1
χ1722222222222-2-2-2-22000022-222-2-2-2-2-222000000-2-20000000000000000002-200000000
χ1822222222222-2-2-2-22000022-222-2-2-2-2-2-2-200000022000000000000000000-2200000000
χ1922222222222-2-2-2-220000-2-2-2-2-22222-22200000022000000000000000000-2-200000000
χ2022222222222-2-2-2-220000-2-2-2-2-22222-2-2-2000000-2-20000000000000000002200000000
χ2122222222-2-2-22222-2222222-2-2-2-2-222-200-2-2-2-222000000000000000000000000000000
χ2222222222-2-2-22222-22222-2-2-22222-2-2-200-2-222-2-2000000000000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-222-2-2-2-2-222-2002222-2-2000000000000000000000000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2-22222-2-2-20022-2-222000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-20000222-2-222-2-22000000000000000000000000002-2002-2000000
χ2622222222-2-2-2-2-2-2-2-20000222-2-222-2-2200000000000000000000000000-2200-22000000
χ2722222222-2-2-2-2-2-2-2-20000-2-2222-2-2222000000000000000000000000002-200-22000000
χ2822222222-2-2-2-2-2-2-2-20000-2-2222-2-222200000000000000000000000000-22002-2000000
χ29222-2-2-22-20002-22-2022-2-20002i−2i2i−2i00000002i−2i0000i2i2−i2−i222−2−2i2i2−i2−i222−2−2000000000000
χ30222-2-2-22-20002-22-2022-2-20002i−2i2i−2i00000002i−2i0000−i2−i2i2i2−2−222−i2−i2i2i2−2−222000000000000
χ31222-2-2-22-20002-22-2022-2-2000−2i2i−2i2i0000000−2i2i0000i2i2−i2−i2−2−222i2i2−i2−i2−2−222000000000000
χ32222-2-2-22-20002-22-2022-2-2000−2i2i−2i2i0000000−2i2i0000−i2−i2i2i222−2−2−i2−i2i2i222−2−2000000000000
χ33222-2-2-22-20002-22-20-2-2220002i−2i2i−2i0000000−2i2i0000i2i2−i2−i222−2−2−i2−i2i2i2−2−222000000000000
χ34222-2-2-22-20002-22-20-2-2220002i−2i2i−2i0000000−2i2i0000−i2−i2i2i2−2−222i2i2−i2−i222−2−2000000000000
χ35222-2-2-22-20002-22-20-2-222000−2i2i−2i2i00000002i−2i0000i2i2−i2−i2−2−222−i2−i2i2i222−2−2000000000000
χ36222-2-2-22-20002-22-20-2-222000−2i2i−2i2i00000002i−2i0000−i2−i2i2i222−2−2i2i2−i2−i2−2−222000000000000
χ372-2-22-2-222000-2-22202-22-22-2000002-200000002-2002−22−22−22−22−22−22−22−2000000000000
χ382-2-22-2-222000-2-22202-22-22-2000002-200000002-200−22−22−22−22−22−22−22−22000000000000
χ392-2-22-2-222000-2-22202-22-2-2200000-220000000-22002−22−2−22−222−22−2−22−22000000000000
χ402-2-22-2-222000-2-22202-22-2-2200000-220000000-2200−22−222−22−2−22−222−22−2000000000000
χ412-2-22-2-222000-2-2220-22-222-2000002-20000000-22002−22−22−22−2−22−22−22−22000000000000
χ422-2-22-2-222000-2-2220-22-222-2000002-20000000-2200−22−22−22−222−22−22−22−2000000000000
χ432-2-22-2-222000-2-2220-22-22-2200000-2200000002-2002−22−2−22−22−22−222−22−2000000000000
χ442-2-22-2-222000-2-2220-22-22-2200000-2200000002-200−22−222−22−22−22−2−22−22000000000000
χ452-2-2-2222-222-2-222-2-22-2-22002000000-2002-20000002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ462-2-2-2222-222-2-222-2-22-2-22002000000-2002-2000000−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ472-2-2-2222-222-2-222-2-2-222-2002000000-200-220000002i−2i−2i2i0000−2i2i2i−2i0000000000000000
χ482-2-2-2222-222-2-222-2-2-222-2002000000-200-22000000−2i2i2i−2i00002i−2i−2i2i0000000000000000
χ492-2-2-2222-2-2-22-222-222-2-2200-2000000200-2200000000002-2-2200002-2-22000000000000
χ502-2-2-2222-2-2-22-222-222-2-2200-2000000200-220000000000-222-20000-222-2000000000000
χ512-2-2-2222-2-2-22-222-22-222-200-20000002002-200000000002-2-220000-222-2000000000000
χ522-2-2-2222-2-2-22-222-22-222-200-20000002002-20000000000-222-200002-2-22000000000000
χ53444-4-4-44-4000-44-44000000004i−4i−4i4i00000000000000000000000000000000000000000
χ54444-4-4-44-4000-44-4400000000−4i4i4i−4i00000000000000000000000000000000000000000
χ5544-444-4-4-44-440000-4000000000000004-4000000000000000000000000000000000000
χ5644-444-4-4-44-440000-400000000000000-44000000000000000000000000000000000000
χ5744-444-4-4-4-44-40000400000000000000000000004i−4i0000000000000000000000000000
χ5844-444-4-4-4-44-4000040000000000000000000000−4i4i0000000000000000000000000000
χ594-44-44-4-444-4-400004000000000000000000000000000000000000000000000022−220000
χ604-44-44-4-444-4-4000040000000000000000000000000000000000000000000000−22220000
χ614-44-44-4-44-4440000-40000000000000000000000000000000000000000000000002i2−2i200
χ624-44-44-4-44-4440000-4000000000000000000000000000000000000000000000000−2i22i200
χ634-4-44-4-44400044-4-4000004-400000-44000000000000000000000000000000000000000
χ644-4-44-4-44400044-4-400000-44000004-4000000000000000000000000000000000000000
χ654-4-4-4444-444-44-4-44-4000000-4000000400000000000000000000000000000000000000
χ664-4-4-4444-4-4-444-4-4440000004000000-400000000000000000000000000000000000000
χ6788-8-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).